MATHEMATICAL ANALYSIS AND NUMERICAL SIMULATIONS FOR THE CANCER TISSUE INVASION MODEL


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Meral G., Yamanlar I. C.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.68, no.1, pp.371-391, 2019 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.31801/cfsuasmas.421546
  • Title of Journal : COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Page Numbers: pp.371-391

Abstract

Cancer cell invasion is one of the most important stages of metastasis. In this paper, the local existence and uniqueness of the cancer cell invasion model is proved using an iterative procedure. Moreover the numerical simulations are performed using a combination of a nonstandard finite difference scheme and backward and forward Euler methods. It is seen that the results agree well with the expected behaviour of the invasion.